Singular

4.19.2 ring declarations

Syntax:

ring name = ( coefficients ), ( names_of_ring_variables ), ( ordering ); or
ring name = cring [ names_of_ring_variables ]

Default:

(ZZ/32003)[x,y,z]

Purpose:

declares a ring and sets it as the actual basering. The second form sets the ordering to (dp,C).

For the second form: cring stands currently for QQ (the rationals), ZZ (the integers) or (ZZ/m) (the field (m prime and <2147483648) resp. ring of the integers modulo m).

The coefficients for the first form are given by one of the following:

1. a cring as given above
2. a non-negative int_expression less or equal 2147483647.
3. an expression_list of an int_expression and one or more names.
4. the name real
5. an expression_list of the name real and an int_expression.
6. an expression_list of the name complex, an optional int_expression and a name.
7. an expression_list of the name integer.
8. an expression_list of the name integer and following int_expressions.
9. an expression_list of the name integer and two int_expressions.

For the definition of the 'coefficients', see Rings and orderings.

'names_of_ring_variables' must be a list of names or (multi-)indexed names.

'ordering' is a list of block orderings where each block ordering is either

1. lp, dp, Dp, rp, ls, ds, Ds, or rs optionally followed by a size parameter in parentheses.

2. wp, Wp, ws, Ws, or a followed by a weight vector given as an intvec_expression in parentheses.

3. M followed by an intmat_expression in parentheses.

4. c or C.

For the definition of the orderings, see Term orderings, Monomial orderings.

If one of coefficients, names_of_ring_variables, and ordering consists of only one entry, the parentheses around this entry may be omitted.

See also Examples of ring declarations; ring; ringlist.